Question

the triangle vwx is a dilation of the triangle vwx. what is the scale factor of the dilation? simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

Step1: Identify corresponding side lengths

Let's consider the vertical side of the triangles. For $\triangle VWX$, the vertical side from $V$ to $X$ has a length of $2 - (- 3)=5$ (counting the grid - squares). For $\triangle V'W'X'$, the vertical side from $V'$ to $X'$ has a length of $3-(-9) = 12$.

Step2: Calculate the scale factor

The scale factor $k$ of a dilation is given by the ratio of the length of a side of the dilated figure to the length of the corresponding side of the original figure. So, $k=\frac{\text{length of side in }\triangle V'W'X'}{\text{length of corresponding side in }\triangle VWX}$. If we take the vertical sides, $k = \frac{12}{3}= 3$.

Answer:

$3$